If your iPhone isn’t activated after it has been restored, it could be from several different issues including the activation server may be temporarily unavailable, iTunes is not recognizing it, or iTunes couldn’t verify it. In order to figure out which problem you are experiencing and how to correct it, it’s easiest to start with the least time consuming activities.
The first thing to do is to restart your iPhone as oftentimes this alone will correct this issue. If that didn’t work, make sure you have the latest version of iTunes and then reconnect your iPhone to iTunes. If iTunes detects your iPhone, it will automatically attempt to activate for you. If that doesn’t work, attempt to restore your iPhone again as the first one may not have restored completely or correctly the first time around.